Research interests

One of the main open questions in our fundamental understanding of the universe is a computa- tional description of strongly coupled phenomenons in Quantum Chromodynamics (QCD). That is, the physical theory that best describes the elementary particles in nature. The theory becomes weakly interacting at short distances or high energies. That is the reason why we can test it and predict with a huge precision the outcome of events in accelerators such as the Large Hadron Collider (LHC) in Switzerland. On the other hand, at low energies or large distances the theory becomes strongly cou- pled and our current textbook tools are not applicable. New mathematical tools are needed to describe strong coupling phenomena such as quark confinement, chiral symmetry breaking and the emergence of a mass gap.

Another fundamental question that has troubled theoretical physicists for decades is how to unify Quantum Field Theory (QFT), that governs the subatomic world, with General Relativity, that governs phenomena at the scale of stars, galaxies or the entire universe. These are two very different scales and therefore, for most questions unification is not needed. However, when we try to address questions such as Black Hole physics or questions about the beginning of the universe, when it was very small and curved, we need to deal with gravity and quantum mechanics at the same time. Doing so requires understanding how gravity emerges as a low energy description of a more fundamental theory. Today, String Theory is the most promising candidate for such an underlying theory that describes gravity in a quantum consistent way.

Remarkably, it turns out that under certain circumstances these two elemental questions are in fact closely related. That is, a certain class of QFTs are equivalent to String theory or Gravity in a space-time with one more spatial dimension. In this holographic duality, the QFT description lives at the boundary of an higher dimensional curved space-time while the gravity dual description of the same theory leaves in the bulk. This spectacular Gauge/Gravity duality is dubbed AdS/CFT. Since its discovery, it has became one of the main theoretical objectives in high energy physics. On one hand, it allows us to address questions in strongly coupled QFT using classical Gravity. On the other hand, it provides us with a complete quantum mechanical description of Gravity and String Theory in a curved background using their dual description in terms of a standard QFT.

My main research interest is to obtain a computational handle on QCD and a deep understanding of quantum gravity. The goal of this proposal is to solve an interacting gauge theory in four dimensions. I expect that such a solution would play an analogues role in QFT to the one played by the Hydrogen atom in chemistry. In 1913 Niels Bohr solved the hydrogen atom. His solution gave rise to an outstanding development in our understanding of atoms and molecules in general. Even though other molecules are not solved exactly, we now have a good computational understanding of them based on our experience from the Hydrogen atom. I believe that an exact solution of an interacting QFT in four dimensions will lead to a similar revolution. In particular, it is expected to greatly improve our understanding of QCD and nature. Moreover, through the AdS/CFT duality it will provide us with the answers to some questions in quantum gravity.

Like the Hydrogen atom in chemistry, we would like to solve the simplest, but still highly inter- acting, QFT. The most established example is of a gauge theory in four space-time dimensions named N =4 Super Yang Mills (SYM). This theory has no length scale, as is typical for critical phenomenon. More precisely, it is scale invariant or in other words, conformal. At the same time, it posses a symmetry between the Bose and Fermi degrees of freedom named supersymmetry. Moreover, it is a beautiful example of a gauge theory in four space-time dimensions that belongs to the class of theories with a gravity dual. Hence, it has an equivalent description in terms of String Theory in a higher dimensional space-time. These properties make it the most tractable gauge theory in four dimensions. Yet, the theory is highly interacting and beyond perturbation theory, new tools are needed for its study. These new tools involve the solvability of the two dimensional string – a surprising and powerful property named integrability. This property is the reason that we expect to be able to solve the four dimensional theory exactly.

With this motivation in mind, my main focus right now is in understanding Correlation Functions, Wilson Loops and Scattering Amplitudes in planar N=4 Super Yang-Mills Theory using Integrability and Holography.